Should be NOT (A k in N)(|U_n {1,...,n}| > k). (Missed thecardinality symbols).

> This is what you claim you can show, right? Well, I think I can> recognize elementary proofs in ZF on their own merits, so I won't> discuss paths. Just show me this proof.-- "It's my belief that when religion and pseudoscience achieve anofficial status within a culture [...], then genocide, war,oppression, injustice, and economic stagnation are sure to follow." -- David Petry, on why |X| < |P(X)| is bad, bad, bad.